Module schemes in invariant theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910436014686208 |
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| author | Brenner, Holger |
| author_facet | Brenner, Holger |
| contents | Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal Cohen-Macaulay R-modules. We establish a correspondence for all linear actions between representations and objects over the invariant ring by looking at quotient module schemes (up to modification) instead of the modules of covariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10592 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Module schemes in invariant theory Brenner, Holger Commutative Algebra Algebraic Geometry Representation Theory 13A50, 13C13, 14L15, 14L24, 14J60, 16T05, 20C99 Let G be a finite group acting linearly on the polynomial ring with invariant ring R. If the action is small, then a classical result of Auslander gives in dimension two a correspondence between linear representations of G and maximal Cohen-Macaulay R-modules. We establish a correspondence for all linear actions between representations and objects over the invariant ring by looking at quotient module schemes (up to modification) instead of the modules of covariants. |
| title | Module schemes in invariant theory |
| topic | Commutative Algebra Algebraic Geometry Representation Theory 13A50, 13C13, 14L15, 14L24, 14J60, 16T05, 20C99 |
| url | https://arxiv.org/abs/2404.10592 |